Abstract:
It is known that with precision till isomorphism that only and only loops $M(F) = M_0(F)/<-1>$, where $M_0(F)$ denotes the loop, consisting from elements of all matrix Cayley-Dickson algebra $C(F)$ with norm 1, and $F$ be a subfield of arbitrary fixed algebraically closed field, are simple non-associative Moufang loops. In this paper it is proved that the simple loops $M(F)$ they and only they are not embedded into a loops of invertible elements of any unitaly alternative algebras if $\text{char} F \neq 2$ and $F$ is closed under square root operation. For the remaining Moufang loops such an embedding is possible. Using this embedding it is quite simple to prove the well-known finding: the finite Moufang $p$-loop is centrally nilpotent.

Abstract:
Let $C(F)$ be a matrix Cayley-Dickson algebra over field $F$. By $M_0(F)$ we denote the loop containing of all elements of algebra $C(F)$ with norm 1. It is shown in this paper that with precision till isomorphism the loops $M_0(F)/<-1>$ they and only they are simple non-associative Moufang loops, where $F$ are subfields of algebraic closed field

Abstract:
It is proved that the maximum condition for subloops in a commutative Moufang loop $Q$ is equivalent with the conditions of finite generating of different subloops of the loop $Q$ and different subgroups of the multiplication group of the loop $Q$. An analogue equivalence is set for the commutative Moufang $ZA$-loops.

Abstract:
It is proved that the following conditions are equivalent for an infinite non-associative commutative Moufang loop $Q$: 1) $Q$ satisfies the minimum condition for subloops; 2) if the loop $Q$ contains a centrally solvable subloop of class $s$, then it satisfies the minimum condition for centrally solvable subloops of class $s$; 3) if the loop $Q$ contains a centrally nilpotent subloop of class $n$, then it satisfies the minimum condition for centrally nilpotent subloops of class $n$; 4) $Q$ satisfies the minimum condition for non-invatiant associative subloops. The structure of the commutative Moufang loops, whose infinite non-associative subloops are normal, is examined.

Abstract:
The structure of the commutative Moufang loops (CML) with minimum condition for subloops is examined. In particular it is proved that such a CML $Q$ is a finite extension of a direct product of a finite number of the quasicyclic groups, lying in the centre of the CML $Q$. It is shown that the minimum conditions for subloops and for normal subloops are equivalent in a CML. Moreover, such CML also characterized by different conditions of finiteness of its multiplication groups.

Abstract:
This paper is a natural continuation of paper "On rectifiable spaces and its algebraical equivalents, topological algebraic systems and Mal'cev algebras" published in arxiv:1309.4572. Thus we justify the need to present the entire material in an unified manner. This paper is the continuation of Section 6 from the first paper. It specifies and corrects the roughest mistakes, incorrect statements and nonsense of the introduced concepts, which are available in numerous papers on topological algebraic systems, basically in papers of Academician Choban M. M. and his disciples.

Abstract:
We investigate the rectifiable spaces, the Mal'cev algebras, the almost quasivarieties of topological algebraic systems and their free systems and others. It specifies and corrects the roughest mistakes, incorrect statements and nonsense of the introduced concepts connected with the concepts listed before, which are available in numerous papers on topological algebraic systems, basically in papers of Academician Choban M.M. and his disciples.

Abstract:
The paper defines the notion of alternative loop algebra F[Q] for any nonassociative Moufang loop Q as being any non-zero homomorphic image of the loop algebra FQ of a loop Q over a field F. For the class M of all nonassociative alternative loop algebras F[Q] and for the class L of all nonassociative Moufang loops Q are defined the radicals R and S, respectively. Moreover, for classes M, L is proved an analogue of Wedderburn Theorem for finite dimensional associative algebras. It is also proved that any Moufang loop Q from the radical class R can be embedded into the loop of invertible elements U(F[Q])of alternative loop algebra F[Q]. The remaining loops in the class of all nonassociative Moufang loops L cannot be embedded into loops of invertible elements of any unital alternative algebras.

Abstract:
The posterior mediastinum, a term synonymous with the paravertebral sulci, is the potential space situated along each side of thevertebral column and adjacent proximal portions of the ribs. The most commonly encountered posterior mediastinal tumors are the neurogenic tumors accounting for 75% of them. The posterior mediastinal tumors may extend into the spinal canal via the intervertebral foramen(dumbbell tumors). These ones account for 10% of the posterior mediastinal tumors and 10% of them are malignant. Due to their presence in two distinct anatomic regions, the thorax and spinalcanal, the surgical treatement of dumbbell tumors require a multidisciplinary approach: thoracic surgeon and neurosurgeon. We present the experience of the Thoracic Surgery Clinic in thesurgery of posterior mediastinal tumors with extension into the spinal canal throughout a 9 year period (2001 – 2010). Seven cases admitted and operated in this period are being analysed.The paper discusses the pathogenic mechanisms, symptoms, diagnosis and treatment of posterior mediastinal tumors with extension into the spinal canal.